Evaluate the improper integral $\int _ { 0 } ^ { \infty } x ^ { - 1 / 2 } d x$
A)4
B)3
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 3 }$

E) $\frac { 1 } { 2 }$

F)2
G)1
H)Divergent

Question

Evaluate the improper integral $\int _ { 0 } ^ { \infty } x ^ { - 1 / 2 } d x$
A)4
B)3
C) $\frac { 1 } { 4 }$ 
D) $\frac { 1 } { 3 }$

E) $\frac { 1 } { 2 }$

F)2
G)1
H)Divergent

Quizplus · Accepted Answer

The integral $\int _ { 0 } ^ { \infty } x ^ { - 1 / 2 } d x$ diverges because the antiderivative of $x^{-1/2}$ is $2x^{1/2}$, and evaluating this from 0 to infinity does not yield a finite value.

Evaluate the Improper Integral ∫0∞x−1/2dx\int _ { 0 } ^ { \infty } x ^ { - 1 / 2 } d x∫0∞​x−1/2dx

Evaluate the Improper Integral $\int _ { 0 } ^ { \infty } x ^ { - 1 / 2 } d x$